There are lots of great choices. I personally like natural oil stones. For rough work I will go with india stones, then fine Arkansas stones for the finish. Others like waterstones but I find water messier as the stones need to soak (not all do, but some do). I find diamond stones are too course but maybe the ultra fine grades are good. Sand paper works well at 1000 and 2000 grit but gets expensive fast as the paper wears out fast.
all of the above work though despite what preferences. you will not go to hell or something for a wrong choice. In the end try soemthing and if it doesn't work for you try something else.
i do have some stones that won't sharpen my exotic wood working blades, but a kitchen knife won't be made of those.